Equivalent T-stub in tension

Componenta de baza a metodei componentelor pentru imbinari cu suruburi (placa de capat, talpa de stalp) — EN 1993-1-8 §6.2.4. Rezistenta analitica = min(Mod 1, Mod 2, Mod 3), plus model cu element finit elastic (deformatie + tensiuni von Mises) generat din datele introduse.

Flange geometry

$F_{Ed}$ kN

$\sum \ell_{eff}$ mm

$t_f$ mm

$m$ mm

$e_{min}$ mm

Flange steel

Bolts

No. of bolts pcs

Diameter

Class

Coefficients

$\gamma_{M0}$

$\gamma_{M2}$

Tool information

What this calculator checks

The calculator determines the tension resistance of an equivalent T-stub, according to EN 1993-1-8 §6.2.4. The T-stub is the basic component of the component method for bolted connections: the flange of an end plate or a column flange, pulled in tension by bolts, is modelled as a T-section loaded in prying.

The three failure modes

A T-stub can fail in three ways, and the resistance is the minimum of them:

Mode 1 — complete flange yielding: $F_{T,1,Rd} = \frac{4 M_{pl,1,Rd}}{m}$ The flange yields along two yield lines (at the bolt and at the root of the fillet) before the bolts fail. Typical for thin flanges with strong bolts — a ductile failure.

Mode 2 — flange yielding + bolt failure: $F_{T,2,Rd} = \frac{2 M_{pl,2,Rd} + n \sum F_{t,Rd}}{m+n}$ A mixed mechanism: the flange yields along one line, and the bolts fail simultaneously.

Mode 3 — bolt failure: $F_{T,3,Rd} = \sum F_{t,Rd}$ The bolts break before the flange yields. Typical for thick flanges — a brittle failure, to be avoided by design.

Prying action

When the flange deforms, it bears on its free edge, generating a prying force that overloads the bolts. The lever arm of this force is $n$ (limited to $1.25\,m$), and its presence is exactly what distinguishes mode 1 from mode 3. A thick flange does not deform, so no prying appears — but then the bolts take the whole force at once (mode 3, brittle). A thinner flange distributes the force through deformation (mode 1, ductile), which is preferable.

Theoretical basis

The analytical resistance here is the check from the platform's CBFEM layer (elastic FEM giving the stress distribution + analytical component check), a Rugarli/xcfem-style approach — an alternative to full solid analysis.

Input data

$F_{Ed}$ — the tension force on the T-stub (kN).
$\ell_{eff}$ — the effective length (from the yield lines), mm.
$m$, $n$ — the geometric distances (bolt–fillet and prying lever arm), mm.
$t_f$ — the flange thickness; $f_y$ — the yield strength.
The bolts — the class, area, tension resistance $F_{t,Rd}$.

Assumptions and limitations

A tension component; shear and bearing are checked separately.
It models a single component of the connection; the full connection combines several T-stubs and components (web, welds).
The effective length $\ell_{eff}$ must be determined from the yield-line patterns matching the configuration.

End plate — the full end-plate connection, modelled with FEM
Beam-to-column connection — a full node, solid CalculiX analysis
Tension resistance — plates with bolt holes